Information on Result #1567317
Linear OOA(25630, 25969, F256, 3, 14) (dual of [(25969, 3), 77877, 15]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(25630, 25969, F256, 2, 14) (dual of [(25969, 2), 51908, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25630, 32773, F256, 2, 14) (dual of [(32773, 2), 65516, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25630, 65546, F256, 14) (dual of [65546, 65516, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25630, 65547, F256, 14) (dual of [65547, 65517, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(25630, 65547, F256, 14) (dual of [65547, 65517, 15]-code), using
- OOA 2-folding [i] based on linear OA(25630, 65546, F256, 14) (dual of [65546, 65516, 15]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OOA(12835, 25969, S128, 3, 14) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(25630, 12984, F256, 6, 14) (dual of [(12984, 6), 77874, 15]-NRT-code) | [i] | OOA Folding | |